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The power of latent variables: How partial least squares can project data into a completely new space?
In statistics, there is a method for solving complex multivariate problems called Partial Least Squares (PLS). This technology is widely used in fields such as chemometrics, bioinformatics and even social sciences. When faced with challenging data, PLS provides researchers with a powerful analytical tool with its unique data projection method.
The core of partial least squares method is to find the potential relationship between predictor variables and response variables.
The main consideration of PLS regression is how to effectively build a prediction model when the number of independent variables exceeds the number of observations. Compared with traditional regression analysis, the advantage of PLS is that it can effectively deal with the problem of multicollinearity. This makes PLS particularly good at performing on high-dimensional data and in situations with multicollinearity.
PLS works by projecting the data into a new space where the covariance between the response variable and the predictor variables is maximized. The PLS model searches for the multidimensional direction in the predictor variable space that can explain the response variable space to the greatest extent. This process makes PLS a bilinear factor model.
Through partial least squares, researchers can more clearly see the underlying structure of the data.
PLS is not only capable of performing regression when the amount of data is huge, it is also effective for classification problems (such as PLS-DA). In the fields of biomedicine and chemistry, PLS is widely used to identify compound features and their classification.
The history of this approach can be traced back to Swedish statisticians Herman Wold and his son Svante Wold. In its initial applications, PLS was mainly used in the social sciences, but over time the method was gradually introduced to other fields such as neuroscience and anthropology.
PLS variants such as OPLS and L-PLS extend the depth of its application and make the model more interpretable and predictive.
After gaining a deeper understanding of the basic architecture of PLS, researchers today have also explored a variety of PLS variants, such as OPLS (Orthogonal Projection to Latent Structure) and L-PLS (Partial Least Squares with L-shaped Parameters). These variants make the data parsing process more refined and more adaptable to specific data types and structures.
PLS's ability to process high-dimensional data makes it an innovative tool in fields such as financial market forecasting and genetic research. Recent developments have combined PLS with single value decomposition (SVD), making this technique capable of performing complex high-dimensional computations on commodity hardware.
With the rapid development of data science, the power of PLS lies not only in the statistical model it proposes, but also in the data potential hidden behind it. The multidimensional data analysis function demonstrated by PLS regression is one of the cornerstones of current artificial intelligence and deep learning applications.
With the advancement of technology, will the application of PLS form a virtuous circle and further promote the cross-integration of multiple fields?
